Prevalence of stable periodic solutions for Duffing equations (Q267465)

If \(X\) is the set of forcing terms \(f(t)\) such that a Duffing equation NEWLINE\[NEWLINE x''+ cx' + g(x) = f(t) NEWLINE\]NEWLINE has at least one T-periodic solution and \(S\) is the subset for which at least one of them is stable. The paper establishes some sufficient conditions for the prevalence of \(S\) on \(X\). Roughly speaking, prevalence is the analogous of full measure set in infinite-dimensional spaces. The conservative (\(c = 0\)) and dissipative (\(c > 0\)) cases are studied separately. The main results cover periodic nonlinearities and Landesman-Lazer conditions and extend some previous results by \textit{R. Ortega} [Adv. Nonlinear Stud. 13, No. 1, 219--229 (2013; Zbl 1278.34042)].